Average Error: 11.9 → 10.8
Time: 28.0s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -1.0730045135916517 \cdot 10^{+126}:\\ \;\;\;\;j \cdot \left(c \cdot t - y \cdot i\right) + \left(\left(\sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x} \cdot \sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x}\right) \cdot \sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x} - \left(b \cdot \left(c \cdot z\right) + \left(i \cdot a\right) \cdot \left(-b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(c \cdot t - y \cdot i\right) + \left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(i \cdot \left(b \cdot \left(-a\right)\right) + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\left(c \cdot b\right) \cdot \sqrt[3]{z}\right)\right)\right)\\ \end{array}\]
\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)
↓
\begin{array}{l}
\mathbf{if}\;b \le -1.0730045135916517 \cdot 10^{+126}:\\
\;\;\;\;j \cdot \left(c \cdot t - y \cdot i\right) + \left(\left(\sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x} \cdot \sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x}\right) \cdot \sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x} - \left(b \cdot \left(c \cdot z\right) + \left(i \cdot a\right) \cdot \left(-b\right)\right)\right)\\

\mathbf{else}:\\
\;\;\;\;j \cdot \left(c \cdot t - y \cdot i\right) + \left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(i \cdot \left(b \cdot \left(-a\right)\right) + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\left(c \cdot b\right) \cdot \sqrt[3]{z}\right)\right)\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r4231359 = x;
        double r4231360 = y;
        double r4231361 = z;
        double r4231362 = r4231360 * r4231361;
        double r4231363 = t;
        double r4231364 = a;
        double r4231365 = r4231363 * r4231364;
        double r4231366 = r4231362 - r4231365;
        double r4231367 = r4231359 * r4231366;
        double r4231368 = b;
        double r4231369 = c;
        double r4231370 = r4231369 * r4231361;
        double r4231371 = i;
        double r4231372 = r4231371 * r4231364;
        double r4231373 = r4231370 - r4231372;
        double r4231374 = r4231368 * r4231373;
        double r4231375 = r4231367 - r4231374;
        double r4231376 = j;
        double r4231377 = r4231369 * r4231363;
        double r4231378 = r4231371 * r4231360;
        double r4231379 = r4231377 - r4231378;
        double r4231380 = r4231376 * r4231379;
        double r4231381 = r4231375 + r4231380;
        return r4231381;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r4231382 = b;
        double r4231383 = -1.0730045135916517e+126;
        bool r4231384 = r4231382 <= r4231383;
        double r4231385 = j;
        double r4231386 = c;
        double r4231387 = t;
        double r4231388 = r4231386 * r4231387;
        double r4231389 = y;
        double r4231390 = i;
        double r4231391 = r4231389 * r4231390;
        double r4231392 = r4231388 - r4231391;
        double r4231393 = r4231385 * r4231392;
        double r4231394 = z;
        double r4231395 = r4231389 * r4231394;
        double r4231396 = a;
        double r4231397 = r4231387 * r4231396;
        double r4231398 = r4231395 - r4231397;
        double r4231399 = x;
        double r4231400 = r4231398 * r4231399;
        double r4231401 = cbrt(r4231400);
        double r4231402 = r4231401 * r4231401;
        double r4231403 = r4231402 * r4231401;
        double r4231404 = r4231386 * r4231394;
        double r4231405 = r4231382 * r4231404;
        double r4231406 = r4231390 * r4231396;
        double r4231407 = -r4231382;
        double r4231408 = r4231406 * r4231407;
        double r4231409 = r4231405 + r4231408;
        double r4231410 = r4231403 - r4231409;
        double r4231411 = r4231393 + r4231410;
        double r4231412 = -r4231396;
        double r4231413 = r4231382 * r4231412;
        double r4231414 = r4231390 * r4231413;
        double r4231415 = cbrt(r4231394);
        double r4231416 = r4231415 * r4231415;
        double r4231417 = r4231386 * r4231382;
        double r4231418 = r4231417 * r4231415;
        double r4231419 = r4231416 * r4231418;
        double r4231420 = r4231414 + r4231419;
        double r4231421 = r4231400 - r4231420;
        double r4231422 = r4231393 + r4231421;
        double r4231423 = r4231384 ? r4231411 : r4231422;
        return r4231423;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Bits error versus j

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if b < -1.0730045135916517e+126

    1. Initial program 6.6

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
    2. Using strategy rm

    3. Applied sub-neg6.6

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    4. Applied distribute-rgt-in6.6

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\left(c \cdot z\right) \cdot b + \left(-i \cdot a\right) \cdot b\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
    5. Using strategy rm

    6. Applied add-cube-cbrt6.7

      \[\leadsto \left(\color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}} - \left(\left(c \cdot z\right) \cdot b + \left(-i \cdot a\right) \cdot b\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    if -1.0730045135916517e+126 < b

    1. Initial program 12.4

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
    2. Using strategy rm

    3. Applied sub-neg12.4

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    4. Applied distribute-rgt-in12.4

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\left(c \cdot z\right) \cdot b + \left(-i \cdot a\right) \cdot b\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
    5. Using strategy rm

    6. Applied distribute-lft-neg-in12.4

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(c \cdot z\right) \cdot b + \color{blue}{\left(\left(-i\right) \cdot a\right)} \cdot b\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    7. Applied associate-*l*11.9

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(c \cdot z\right) \cdot b + \color{blue}{\left(-i\right) \cdot \left(a \cdot b\right)}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    8. Taylor expanded around inf 11.1

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{z \cdot \left(b \cdot c\right)} + \left(-i\right) \cdot \left(a \cdot b\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
    9. Using strategy rm

    10. Applied add-cube-cbrt11.2

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}\right)} \cdot \left(b \cdot c\right) + \left(-i\right) \cdot \left(a \cdot b\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    11. Applied associate-*l*11.2

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \left(b \cdot c\right)\right)} + \left(-i\right) \cdot \left(a \cdot b\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification10.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.0730045135916517 \cdot 10^{+126}:\\ \;\;\;\;j \cdot \left(c \cdot t - y \cdot i\right) + \left(\left(\sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x} \cdot \sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x}\right) \cdot \sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x} - \left(b \cdot \left(c \cdot z\right) + \left(i \cdot a\right) \cdot \left(-b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(c \cdot t - y \cdot i\right) + \left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(i \cdot \left(b \cdot \left(-a\right)\right) + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\left(c \cdot b\right) \cdot \sqrt[3]{z}\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))